Geometry Questions for SSC CGL

Triangle Basics and Key Theorems

Triangles dominate geometry questions. You must know angle-sum property, exterior angle theorem, and side inequalities cold. The exterior angle of a triangle equals the sum of the two non-adjacent interior angles — this single rule solves dozens of SSC questions directly without full calculation.

• Sum of all angles in a triangle = 180 degrees
• Exterior angle = sum of two remote interior angles
• Sum of any two sides > third side (triangle inequality)
• In a right triangle, the hypotenuse is the longest side
• Pythagoras triples to memorise: 3-4-5, 5-12-13, 8-15-17, 7-24-25
• Median divides a triangle into two equal area triangles

Triangle Similarity and Congruence

SSC CGL loves questions where two triangles are similar and you must find a missing side or area ratio. The key rule: if triangles are similar with ratio k, their areas are in ratio k squared. Congruence (SSS, SAS, ASA, RHS) occasionally appears in reasoning-style geometry questions.

• AA (Angle-Angle) is the most common similarity criterion in SSC questions
• Corresponding sides of similar triangles are proportional
• Area ratio of similar triangles = square of side ratio
• Basic Proportionality Theorem (BPT): line parallel to one side divides other two sides proportionally
• Mid-point theorem: line joining midpoints of two sides is parallel to third side and half its length

Triangle Centres (Most Tested in SSC CGL)

SSC CGL repeatedly asks about the four triangle centres. Remember each centre's definition and its special angle property, especially for incentre and orthocentre — the angle formulas are direct MCQ fodder.

• Centroid: intersection of medians. Divides each median in 2:1 from vertex.
• Incentre: intersection of angle bisectors. Always inside the triangle.
• Circumcentre: intersection of perpendicular bisectors. Equidistant from all vertices.
• Orthocentre: intersection of altitudes. Can be outside (obtuse triangle).
• Incentre angle formula: angle BIC = 90 + (A/2)
• Orthocentre angle formula: angle BOC = 180 - A (where O is orthocentre)

Circles: Chords, Tangents and Angles

Circle questions are extremely frequent. The most tested rules are: tangent is perpendicular to radius at point of contact, two tangents from external point are equal, and the angle in a semicircle is 90 degrees. The inscribed angle theorem (angle at centre = twice angle at circumference) is a single rule that solves a whole category of questions.

• Tangent from external point: two tangents are equal in length
• Tangent-radius angle = 90 degrees always
• Angle in semicircle = 90 degrees (Thales theorem)
• Inscribed angle = half the central angle on same arc
• Angles in same segment are equal
• Cyclic quadrilateral: opposite angles sum to 180 degrees

Quadrilaterals and Polygons

SSC tests properties of parallelogram, rhombus, rectangle, square, and trapezium. The diagonal properties and area formulas are the most asked. For regular polygons, the interior angle formula is directly applied in one-step questions.

• Parallelogram: opposite sides equal, diagonals bisect each other
• Rhombus: all sides equal, diagonals bisect at 90 degrees
• Rectangle: all angles 90 degrees, diagonals are equal
• Square: all sides equal + all angles 90 degrees
• Trapezium area = (1/2) x (sum of parallel sides) x height
• Interior angle of regular n-gon = (n-2) x 180 / n

• Confusing incentre and circumcentre angle formulas: Incentre gives 90 + A/2, Circumcentre gives 2A — mixing these costs marks every year.
• Forgetting that the area ratio of similar triangles is the SQUARE of the side ratio, not the ratio itself.
• Assuming orthocentre is always inside the triangle — it goes outside for obtuse triangles and lands on the right-angle vertex for right triangles.
• In tangent-secant problems, using PT = PB instead of PT^2 = PB x PC — a very common algebraic slip under time pressure.
• For cyclic quadrilaterals, adding all four angles instead of using opposite angles sum to 180 degrees.

• CICO for triangle centres order from always-inside to sometimes-outside: Centroid Inside, Circumcentre can go outside (obtuse), Orthocentre definitely outside (obtuse). Incentre is ALWAYS inside — think I = Inside.
• For incentre angle: BIC = 90 + half of A. Think 'I add 90 and take half' — the incentre is generous, it adds 90.
• Tangent-secant rule: PA squared = near times far (PB is near, PC is far on secant). Square the solo, multiply the pair.
• SRAS mnemonic for rhombus: Sides equal, Right angles at diagonals, Area = half product of diagonals, Sides bisect angles.

• SSC CGL typically places 4-6 geometry questions in Tier 1 Quant. Expect 1-2 on triangle centres (especially incentre angle), 1-2 on circle tangents/chords, and 1 on similar triangles area ratio.
• Triangle centre questions in recent papers (2022-2024) almost always give you one angle and ask for the angle at a specific centre — memorise the three formulas and you solve these in under 30 seconds.
• Circle questions frequently use the tangent-secant power rule or ask for the angle subtended at centre vs circumference. Draw a quick diagram — it reveals the theorem instantly.
• Avoid deriving from scratch under exam pressure. These are theorem-recall questions, not derivation questions. If you cannot recall the theorem in 10 seconds, mark and move on.
• For quadrilateral area questions, check if it is a rhombus first (all sides equal) — the diagonal formula is the fastest route. Trapezium area is the second most tested shape in this category.